There are basically three different types of backup: Full Backup, Incremental Backup and Differential Backup. You can read more about those here:
An easy way to backup is using rsync. Here is a neat tutorial:
I would recommend you to read about those three different procedures of backing up a system and then choose one that works best for you. When you've done that, google, for example: "Linux Differential Backup". Some links should be some tutorials to guide you through it.
I personally don't use any automatic way of backing up my system. All I use are two linux tools (tar and gzip) to do a Full Backup / Restore (Note: not backup/restore of the whole system, only my personal files). Take a look in here to see how I do it:
It really depends how you want to backup your files, how often they change and how big they are.